Replicating double-sided normals on a cube face, extruding causes inner faces
it's impossible to have two normals per face. (you can check out the documentation of how the mesh datablock is designed)

The only way you can get this situation is if you managed to duplicate the face. (Shift-D for example) So you do have two faces overlapping, facing in different directions. You can verify that by selecting one face and then moving it away, the other one will stay. 

Of course I can't really tell what you did in that particular scene.